Exact conservation laws, i.e. first integrals of the full dynamics, were
already used for model order reduction. If such quantities exist, one
can eliminate a number of variables and equations equal to the number of
independent conservation laws [1]}, [2]}.
In the present work, we introduce the approximate conservation laws
that are quantities conserved by the fast dynamics.
For many CRNs, the number of approximate conservation laws supersedes that
of exact conservation laws, allowing for important reduction.
We thus provide algorithmic reduction methods covering the case of non-hyperbolic fast dynamics with conservation.
Our algorithms are inspired from the
quasi-equilibrium approximation
that is well known for chemical reaction networks [3]}, [4]}.
Contrary to the quasi-equilibrium approximation that uses only linear approximate conservation laws, here we are also exploiting non-linear conserved quantities. Similar ideas were developed in [5]}, [6]},
but without a full algorithmic solution. Like in [7]} we use tropical geometry to find appropriate time and concentration scales in this case as well.
